few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Understand similarity in terms of similarity transformations.

Make geometric constructions.

Understand and apply theorems about circles.

Apply geometric concepts in modeling situations.

Prove geometric theorems.

Use coordinates to prove simple geometric theorems algebraically.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

Analyze, compare, create, and compose shapes.

Classify two-dimensional figures into categories based on their properties.

Explain volume formulas and use them to solve problems.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Translate between the geometric description and the equation for a conic section.

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Solve real-world and mathematical problems involving area, surface area, and volume.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Understand and apply the Pythagorean Theorem.

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Visualize relationships between two-dimensional and three-dimensional objects.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Reason with shapes and their attributes.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
problem_activity: Task
The goal of this task is to explain why the area enclosed by a circle $C$ of radius $r$ is
$\pi r^2$.  Recall that $\pi$ is the ratio of the circumference of a circle to its diameter and that this ratio is independent of the size of the circle.
Draw a picture of a regular octagon $O$ inscribed in $C$.  Find  a formula for the area of the octagon in terms of its perimeter.
Reasoning as in part (a), find a formula for the area of a regular $n$ sided polygon, for $n \geq 3$, inscribed in $C$: the formula should give the area of the polygon  in terms of  its perimeter.
Using your formula from part (b), explain why the area of $C$ is $\pi r^2$.


correct_option_index: 11